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yawa3891 [41]
4 years ago
5

The mean per capita consumption of milk per year is 140 liters with a standard deviation of 22 liters. If a sample of 233 people

is randomly selected, what is the probability that the sample mean would be less than 137.01 liters? Round your answer to four decimal places.
Mathematics
1 answer:
salantis [7]4 years ago
4 0

Answer: 0.0192

Step-by-step explanation:

Given : The mean per capita consumption of milk per year : \mu=140\text{ liters}

Standard deviation : \sigma=22\text{ liters}

Sample size : n=233

Let \overline{x} be the sample mean.

The formula for z-score in a normal distribution :

z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}

For  \overline{x}=137.01

z=\dfrac{137.01-140}{\dfrac{22}{\sqrt{233}}}\approx-2.07

The P-value = P(\overline{x}

Hence, the probability that the sample mean would be less than 137.01 liters is 0.0192 .

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